Quantum Circuits with Unbounded Fan-out

We demonstrate that the unbounded fan-out gate is very powerful. Constant-depth polynomial-size quantum circuits with bounded fan-in and unbounded fan-out over a fixed basis (denoted by QNC0 f ) can approximate with polynomially small error the following gates: parity, mod[q], And, Or, majority, threshold[t], exact[q], and counting. Classically, we need logarithmic depth even if we can use unbounded fan-in gates. If we allow arbitrary one-qubit gates instead of a fixed basis, then these circuits can also be made exact in log-star depth. Sorting, arithmetical operations, phase estimation, and the quantum Fourier transform can also be approximated in constant depth.

• Type: Journal
• Year: 2002
• Where: CORR
• Authors: Peter Høyer, Robert Spalek
• Keywords: CORR 2002, Education, Fixed Basis, Unbounded, Unbounded Fan-out Gate